Fanelo James Arens: Master of Commerce Dissertation, University of Cape Town 1 THE ALTMAN CORPORATE FAILURE PREDICTION MODEL: APPLIED AMONGST SOUTH AFRICAN MEDICAL SCHEMES By Fanelo James Arens (ARNFM001) A DISSERTATION Submitted to THE UNIVERSITY OF CAPE TOWN Department of Finance and Tax In partial fulfillment of the requirements for the degree of MASTER OF COMMERCE IN FINANCE (Specializing in Financial Management) 2014 Supervisor: Darron West
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Fanelo James Arens: Master of Commerce Dissertation, University of Cape Town
1
THE ALTMAN CORPORATE FAILURE PREDICTION MODEL: APPLIED
AMONGST SOUTH AFRICAN MEDICAL SCHEMES
By
Fanelo James Arens (ARNFM001)
A DISSERTATION
Submitted to
THE UNIVERSITY OF CAPE TOWN
Department of Finance and Tax
In partial fulfillment of the requirements for the degree of
MASTER OF COMMERCE IN FINANCE
(Specializing in Financial Management)
2014
Supervisor: Darron West
Fanelo James Arens: Master of Commerce Dissertation, University of Cape Town
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Declaration
I hereby declare that this paper constitutes my own work and that through extensive
literature research; ideas, expressions, writings or findings of others have been
incorporated, for which appropriate credit has been given.
Signature ………………………………………………
Fanelo James Arens
Fanelo James Arens: Master of Commerce Dissertation, University of Cape Town
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ABSTRACT
THE ALTMAN CORPORATE FAILURE PREDICTION MODEL: APPLIED
AMONGST SOUTH AFRICAN MEDICAL SCHEMES
This study has a number of interrelated objectives that seek to understand and
contextualize the Altman bankruptcy prediction model in the setting of the South African
medical schemes over a ten year period (2002 to 2011). The main objective of this
study is to validate the Altman Z2 model amongst the medical schemes in South Africa;
in terms of accurately classifying Z2-scores of ≤ 1.23 and ≥ 2.9 into the a priori groups of
failed and non-failed schemes.
The average classification rates in the period 2002 to 2011 are as follows: 82%
accuracy rate and 17.9% error rate. A linear trend line inserted in the graph shows the
accuracy improving from 72% to 91% between the period 2003/2004 to 2011/2012.
This outcome is consistent with the conclusion in previous studies (Aziz and Humayon,
2006: 27) that showed the accuracy rates in most failure prediction studies to be as
follows: 84%, 88%, and 85% for statistical models, AEIS models and theoretical models
respectively.
Although this study validated the Altman model, further studies are required to test the
rest of the study objectives under conditions where some of the assumptions are
revised.
.
By
Fanelo James Arens
Fanelo James Arens: Master of Commerce Dissertation, University of Cape Town
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ACKNOWLEDGEMENTS
My sincere gratitude goes to my supervisor Darron West (from the University of Cape
Town (UCT) – department of Finance and Tax) for his insights, encouragement and
guidance in making such a daunting task purposeful and exciting. I am grateful and
indebted to Moleboheng Molabe (from the Council for Medical Schemes) for patiently
guiding me through the CMS‟s financial reporting formats. I am also thankful to Roshan
Nambafu for meticulously organizing and constructing the database for the study. This
task would have been impossible without the expert input of Katya Mauff (UCT
Department of Statistical Sciences). This section would not be complete without the
acknowledgement of my sources of inspiration; my wife Grizelda Arens, my daughter
Lucksy and two sons Fanelo and Monde.
Fanelo James Arens: Master of Commerce Dissertation, University of Cape Town
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Table of Contents
TABLE OF CONTENTS ....................................................................................................................................................... 5
1.1. FAILURE OF SIGNIFICANT MEMBERSHIP GROWTH AMONGST SA MEDICAL SCHEMES ........................................................ 9
1.2. HIGH MEDICAL INFLATION AND ITS CONTRIBUTING FACTORS..................................................................................... 10
1.3. HIGH BURDEN OF DISEASE IN SOUTH AFRICA ......................................................................................................... 13
1.4. AGING OF THE MEDICAL SCHEME POPULATION ...................................................................................................... 14
1.6. PORTER’S FIVE FORCES COMPETITIVE MODEL: IN THE HEALTH CARE INDUSTRY .............................................................. 16
1.6.1. THREAT OF NEW ENTRANTS ............................................................................................................................... 16
1.6.2. THREAT OF SUBSTITUTION ................................................................................................................................ 17
1.6.3. BARGAINING POWER OF SUPPLIERS .................................................................................................................... 17
1.6.4. BARGAINING POWER OF CUSTOMERS .................................................................................................................. 19
1.7. SOLVENCY LEVELS OF MEDICAL SCHEMES ............................................................................................................. 20
1.8. SUMMARY OF INTRODUCTION ........................................................................................................................... 21
1.9. OBJECTIVE OF THE STUDY ................................................................................................................................. 22
2. LITERATURE REVIEW ........................................................................................................................................ 23
2.1. POSSIBLE CAUSES OF BUSINESS FAILURES ............................................................................................................. 23
2.2. STATISTICAL BASIS OF THE EARLIER BUSINESS FAILURE PREDICTION MODELS ................................................................. 26
2.3. BRIDGING THE GAP BETWEEN FINANCIAL RATIO ANALYSIS AND THE MORE RIGOROUS STATISTICAL TECHNIQUES .................. 26
2.4. UNIVARIATE VS. MULTIVARIATE ANALYSIS MODELS ................................................................................................ 27
2.5. DESCRIPTION OF COMMONLY USED STATISTICAL FAILURE PREDICTION MODELS ............................................................ 28
2.6. THE ALTMAN Z-SCORE ..................................................................................................................................... 29
2.7. DESCRIPTIONS OF THE RATIOS USED IN THE ALTMAN Z-SCORES ................................................................................. 31
2.8. THE RELEVANCE OF ALTMAN MODELS IN MODERN DAY PREDICTION OF COMPANY FAILURES ........................................... 33
2.9. ALTERNATIVE POPULAR MODELS: SURVIVAL ANALYSIS, DECISION TREES AND NEURAL NETWORKS .................................. 35
2.10. PREDICTION MODELS WITH A FINANCIAL STATEMENT ANALYSIS LOGIC........................................................................ 36
2.11. THEORETICAL DEBATES AROUND THE EARLIER BANKRUPTCY MODELS .......................................................................... 39
2.12. GENERALIZABILITY OF THE ALTMAN Z-SCORE ........................................................................................................ 39
2.13. GENERAL LIMITATIONS OF PREDICTION FAILURE MODELS ......................................................................................... 42
2.14. SUMMARIES OF THEMES: MAIN ARGUMENTS AND REBUTTALS .................................................................................. 43
3. RESEARCH METHODOLOGY .............................................................................................................................. 45
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3.1. DATA SELECTION AND PREPARATION ................................................................................................................... 45
3.2. SPECIAL CONSIDERATIONS AND ASSUMPTIONS IN DATA SELECTION ............................................................................ 46
3.3. SAMPLE SELECTION AND TIME PERIOD ................................................................................................................. 47
3.4. VARIABLE SELECTION AND ADJUSTMENTS ............................................................................................................. 48
3.5. PRACTICAL STEPS IN THE METHODOLOGY .............................................................................................................. 49
3.5.1. CALCULATION OF ACCURACY (CLASSIFICATION AND ERROR RATES) ............................................................................. 51
3.5.2. METHODOLOGY USED FOR REESTABLISHING ALTERNATIVE Z-SCORES WAS AS FOLLOWS ................................................. 52
4.2. VALIDATION OF THE ALTMAN Z-SCORE IN THE SA MEDICAL SCHEME INDUSTRY............................................................ 54
4.3. COMPARING VARIABLES AND Z-SCORES OF FAILED AND NON-FAILED SCHEMES ............................................................. 55
4.4. CORRELATION BETWEEN THE INDEPENDENT VARIABLES AND THE Z-SCORES ................................................................. 56
4.5. ACCURACY OF THE ALTMAN PREDICTION MODEL AMONGST SA MEDICAL SCHEMES ...................................................... 58
4.6.1. ACCURACY AND ERROR RATES CALCULATIONS WITH GREY AREA COUNTS INCLUDED ....................................................... 58
4.6.2. ACCURACY AND ERROR RATE CLASSIFICATIONS EXCLUDING THE GREY AREA COUNTS ...................................................... 61
4.7. RE-ESTIMATED COEFFICIENTS: RERUNNING THE MDA USING ORIGINAL VARIABLES ....................................................... 62
4.8. CLASSIFICATION TABLES OF THE NEW MEDICAL SCHEME Z-SCORE (MS_Z-SCORE) ........................................................ 62
4.9. THE NEW EQUATION RESULTING FROM THE RE-ESTIMATION OF COEFFICIENTS .............................................................. 64
4.9.1. MEDIANS OF THE MS_Z VALUES OF THE FAILED AND NON-FAILED SCHEMES ............................................................... 65
4.9.2. CUT-OFF VALUES FOR NEW MS_Z-SCORE ............................................................................................................ 66
4.10. ALTERNATIVE Z-VALUES (ALT_MS-SCORES): RERUNNING MDA USING NEW VARIABLES ............................................... 67
4.10.1. ACCURACY OF THE ALT_MS_Z-SCORES IN THE FAILED AND NON-FAILED SCHEMES ....................................................... 68
4.10.2. THE ALTERNATIVE EQUATION RESULTING FROM NEW VARIABLES ............................................................................... 71
4.10.3. CUT-OFF VALUES FOR ALT_MS_Z-SCORE ............................................................................................................ 71
5.1. COMPARING VARIABLES OF FAILED AND NON-FAILED SCHEMES ................................................................................. 74
5.2. CORRELATION OF VARIABLE WITH THE Z-SCORE ..................................................................................................... 75
5.3. PERFORMANCE OF MDA MODEL IN THE SA MEDICAL SCHEME INDUSTRY ................................................................... 76
5.3.1. CLASSIFICATION AND ERROR RATES WITH GREY ZONE COUNTS INCLUDED .................................................................... 76
5.3.2. CLASSIFICATION AND ERROR RATES WITH GREY ZONE COUNTS EXCLUDED .................................................................... 76
5.3.3. THE NEW AND ALTERNATIVE Z-SCORES ................................................................................................................ 77
9.1. ANNEXURE A .................................................................................................................................................. 85
9.2. ANNEXURE B .................................................................................................................................................. 86
9.3. ANNEXURE C .................................................................................................................................................. 87
9.4. ANNEXURE D ................................................................................................................................................. 88
9.5. ANNEXURE E .................................................................................................................................................. 89
Fanelo James Arens: Master of Commerce Dissertation, University of Cape Town
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1. Introduction
South African (SA) medical schemes constitute a significant sector of the economy in
terms of the number of schemes as well as the reserves under management. As at 31
December 2011 “there were 97 medical schemes (26 open and 71 restricted),
representing a total of 8 526 409 lives” (Council for Medical Schemes (CMS) annual
report, 2011: 114). In 2011 schemes managed a total combined fund of R36.8 billion,
13% higher than 2010.
Medical schemes operate as not for profit organizations regulated under the Medical
Schemes Act, No. 131 of 1998. There has not been any significant change in the
competitive structure as well as service delivery model of this sector since the birth of
democracy in South Africa. The sector and the entire health care industry have thus not
delivered on the national aspirations of achieving equitable and affordable health care
for all South Africans. This realization has driven the ruling party and South African
government to consider an alternative healthcare funding and delivery model in the form
of National Health Insurance (NHI), which is in its advanced stages of conceptualization
and early stages of implementation. The NHI will in all likelihood expedite an
unprecedented consolidation in the medical scheme sector that will result in a few
surviving schemes that sell augmented services not provided for in the NHI benefit
structure.
This section will provide a background to the problems the medical scheme sector is
currently facing, which are: failure of significant growth in membership, high medical
inflation and its contributing factors, the high burden of disease in South Africa, the
competitive structure of the private health care industry as well as the role of the
solvency ratios as a tool to monitor schemes‟ capital adequacy.
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1.1. Failure of significant membership growth amongst SA medical schemes
Membership growth of medical schemes remained stagnant between 2000 and 2004
(Exhibit 1). The growth observed between 2005 and 2011 was in the restricted
schemes (employer schemes) whilst there was a decline in numbers in open schemes
(CMS annual report, 2011: 114). The Government Employee Medical Scheme (GEMS),
which is a restricted scheme, largely accounted for this growth. During this period (2005
to 2011) the number of beneficiaries grew from just under 7 million to around 8.5 million.
Exhibit 1: Trend in number of beneficiaries on medical schemes (2000 to 2011)
CMS Annual Report (2011: 114)
Open schemes showed negative growth between 2006 and 2011. This trend could be
because open schemes are voluntary and are therefore susceptible to loosing members
Fanelo James Arens: Master of Commerce Dissertation, University of Cape Town
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during difficult economic times as experienced in the period 2007 to 2011. Medical
schemes spend a significant amount of money on marketing. In 2011 the brokerage
costs (for all schemes) was R1.4 billion; a 5% increase from 2010 (CMS annual report,
2011: 134). Despite these exorbitant marketing fees, there has been no significant
growth in total membership of the sector over the last ten years.
1.2. High medical inflation and its contributing factors
High medical inflation is one of the main factors contributing to the failure of the private
health care system in South Africa. The current private health care financing system is
the root cause of the runaway inflation. Aragua and McIntyre (2012: 1) observed that
the South African health care system has “an overall progressive financing system but a
pro-rich distribution of health care benefits”. The above authors lament that the South
African private health care system mainly covers a small portion of the population that is
mainly rich (Ataguba & McIntyre, 2012: 1). The authors observe that this small rich
group that benefits the most from the health care system has the lowest share of the
disease burden. The above observation has major implications for our healthcare
system and the sustainability of medical schemes in the private environment. It in effect
means that the current healthcare system is inequitably accessed and that resources
are, as a result, inequitably distributed. The behaviour of suppliers is typically influenced
very strongly by the incentives created by the payment mechanism in the health care
system (Mackintosh, 2003: 19). The current healthcare system is to a large extent
supply based rather than needs and demand based. High income health care systems,
such as is found in South Africa, have strong commercial elements on the supply side
(Mackintosh, 2003: 17). Service providers such as specialist are the main drivers of the
supply side. This may present a conflict of interest on the part of the service providers
who are in a position to prescribe a healthcare intervention from which they are likely to
derive economic benefits.
The medical scheme sector has ninety seven individual schemes (as at 2011), all of
Fanelo James Arens: Master of Commerce Dissertation, University of Cape Town
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which provide very similar products. There is often no distinct value differentiation
amongst the schemes and options. Individual schemes, some of which are very small,
are often not in a position to negotiate competitive tariff rates with the large South
African hospital groups, which are displaying the characteristics of an oligopoly
(Germishuizen, 2009: 38). Medical schemes are therefore price takers whilst hospitals
are price setters.
Medical schemes are also under pressure from substitute products like hospital plans
offered by mainstream insurance companies. The products are often competitively
priced as they are not governed by and exposed to the risk of prescribed minimal
benefit (PMB) legislation (Medical Scheme Act (MSA) 131 of 1998), which prescribes
that schemes have to pay in full (at the price quoted by the service providers) for all
PMB conditions. The PMB legislation poses a major risk to medical schemes as the
provisions of the legislation lend themselves to abuse by service providers. According to
the Towers Watson survey report (2012: 6) the top three global healthcare cost drivers
are medical technology cost (52%), overuse of healthcare by service providers (50%)
and profit motive of service providers (31%) in that order.
In addition to the PMB legislation, medical schemes can no longer choose their
members or discriminate against members on the bases of claiming patterns, disease
profile or family size. Survival of medical schemes is therefore dependent upon the skill
and technology the medical scheme possesses to mitigate claims risk. It has been
established, that “the number of chronic beneficiaries in a family is an important risk
factor if a member is classified into a normal claiming category or an above-normal
claiming category” (De Villiers, Van der Merwe & Van Wyk Kotze, 2004). In addition to
the skill and technology mentioned above, there needs to be definitive efforts, such as
disease management programs that specifically address specific disease burdens as
well as compliance to medications and treatment plans. Smaller schemes are not
always in a financial position to afford these risk mitigating measures. Even for those
that can afford them, the success of these measures are not always easily discernible
and quantifiable, hence scheme executives do not always regard them as priority.
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Healthcare cost is one of the factors that necessitated the government to consider
alternative healthcare funding and delivery methods. In their study, Pillay & Skordis-
Worrall (2013: 326) identified certain factors that could have determined the agenda
setting process for healthcare reform in South Africa such as: “a change in government,
increase in the cost of private medical schemes, and increase in support for reform from
various stakeholders”. The framework below (Exhibit 2) illustrates all other contributing
factors in the policy agenda setting process.
Exhibit 2: Health care reform agenda setting process in South Africa
Source: Pillay & Skordis-Worrall (2013: 326)
Medical schemes have been casualties of this escalating healthcare cost, with a
number of schemes having had to close down or merge into other schemes. The private
healthcare cost is indeed essential in this framework as it is likely to undermine any
government initiatives to attaining equitable and affordable healthcare for all South
African citizens. Hence all government efforts are targeted at containing the escalating
healthcare costs and this, in government‟s view, will finally be achieved by the
Fanelo James Arens: Master of Commerce Dissertation, University of Cape Town
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introduction of the National Health Insurance (NHI) (Dept. of Health, South Africa, 2011:
32).
It does appear at this stage that the NHI will play a significant role in both the financing
and provision of health care. The role of medical schemes in the financing of healthcare
has not been well elucidated by the authorities thus far. Some antagonists of the NHI
feel that the susceptibility of the healthcare system to regulation presents an opportunity
for policymakers to “achieve social protection objectives through the strategic
management of markets rather than exclusively through less responsive systems based
on tax funded direct provision” (van den Heever, 2012: 12).
1.3. High burden of disease in South Africa
The Lancet Special Report (2009: 4, 5) highlights the major healthcare challenges and
pressures also known as the burden of disease. The following are the elements of the
so called Quadruple Burden of Disease, according to the Lancet report (2009), currently
plaguing the South African health care system:
(i) Maternal, newborn and child health: 1% of global burden (2–3 x average for
comparable income countries)
(ii) Non-communicable disease: < 1% of global burden (2-3 x higher than
average for developing countries)
(iii) HIV/AIDS and Tuberculosis (TB): 177% of HIV global burden (23 x global
average) 5% of global TB burden (7 x global average)
(iv) Violence and injury: global burden of injuries (2x global average for injuries
per capita, 5 x global average homicide rate)
The above categories of disease burdens are way above global averages of peer
countries, particularly Human Immunodeficiency Virus / Acquired Immunodeficiency
Disease (HIV and AIDS) and TB. SA has shown no progress in reaching the Millennium
Development Goals (MDGs) and has instead regressed in some of the goals (The
Fanelo James Arens: Master of Commerce Dissertation, University of Cape Town
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Lancet 2009: 4, 5). It is important to note that most countries have only one or at most
two categories of Burden of Disease compared to SA which owns four; hence the
quadruple burden of disease.
1.4. Aging of the medical scheme population
Members of open schemes have demonstrated a significant aging pattern from 2007 to
2010 (Exhibit 3). There are a number of factors that has led to this trend. The life span
of the general population has increased as a result of the life-saving medicines
introduced to the South African market in the past twenty years. The success of the
Antiretroviral (ARV) treatment program has also played a significant role in curbing
unnecessary morbidity and mortality from HIV and Aids. Open schemes are more
vulnerable to the above phenomenon as the age of restricted scheme members is
influenced and limited by the retirement age of the working population.
Fanelo James Arens: Master of Commerce Dissertation, University of Cape Town
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Exhibit 3: Aging trend in medical schemes of SA
Source: CMS Annual Report, (2011: 159)
1.5. Product
There is very little differentiation in the products available to potential medical scheme
members, as all schemes offer very similar products. The options within the schemes
range from low cost: which mainly cater for PMBs to high-end: offering more benefits in
categories such as chronic medicines for non-PMB conditions, optical and dental
benefits as well as higher specialist fees. The problem medical schemes face is that
there is no real tangible value offering that differentiates one scheme from the other.
This makes it easy for members to switch scheme once they encounter a situation
where another scheme seems to reimburse better for the condition that they intend
Fanelo James Arens: Master of Commerce Dissertation, University of Cape Town
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claiming for in the near future. Some of the competitive strategies employed by medical
schemes are product augmentation with supplementary services such gym
memberships and discounts on other insurance products. The MSA 131 of 1998 clearly
defines the business of a medical scheme and hence most schemes are unable to form
the above strategic partnerships.
1.6. Porter’s five forces competitive model: in the health care industry
Analyzing the medical scheme industry using the Porter five forces competitive model
clearly illustrates the structural problems in the industry; and perhaps also hints that
these problems are unlikely to be resolved to any degree by market forces. The
following are the elements of the Porter model that will be briefly described in the
context of the SA medical scheme and health care industries:
— Threat to new entrants
— Threat to substitution
— Bargaining powers of suppliers
— Bargaining powers of customers
1.6.1. Threat of new entrants
Since medical schemes are not for profit organization, their capital is derived from
membership contributions. The establishment of such organizations has been easy in
the past, with no real barriers to entry; hence the high number of medical schemes in
the country in earlier years. Since medical schemes are strictly governed by the Medical
Schemes Act 131 of 1998, their business models are similar and in the public domain.
In recent years, solvency levels have been dropping, dipping below the target figure of
Fanelo James Arens: Master of Commerce Dissertation, University of Cape Town
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25%. Because of the protracted high unemployment rates at and above 24% between
2009 and 2011 (Statistics SA. 2011), as well as inability of the schemes to compete on
the basis of innovation, this sector has started to become unattractive and hence has
not been attracting new entrants in quite a while and instead the number of schemes
has been reducing as a result of business failures and mergers (Exhibit 16: p58).
1.6.2. Threat of Substitution
Alternative health insurance products such as hospital plans offered by traditional
insurance houses have been a constant threat to the medical scheme sector. There
have also been a growing number of insurance products that cover the shortfall
between what the service provider charges and what medical schemes pay for non-
PMB conditions. These products have the effect that members may buy down to lower
options with lessor cover for non-PMB conditions.
1.6.3. Bargaining power of suppliers
Because of the concentration of main suppliers such as the hospitals, with effectively
only four big groups (Netcare, Mediclinic, Life Health and NHN), medical schemes don‟t
have any bargaining power and therefore reimbursement tariffs (prices) are dictated by
the hospital groups. This is evidenced by the un-abating increase in the private hospital
cost portion of medical schemes from 2000 to 2011 as illustrated by the Exhibit 4
below. Note the sustained growth in hospital and specialist costs from 2000 to 2011.
The prices of medicines (red line) abated from 2001 with the introduction of Single Exit
Pricing (SEP) to the pharmacy sector. The government has established a commission
of enquiry, as of Jan 2014, that will investigate and possibly recommend on the reasons
for and solutions to the runaway healthcare costs in South Africa. The commission is
expected to finalize its mandate and produce a report by the end of 2015.
Fanelo James Arens: Master of Commerce Dissertation, University of Cape Town
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Exhibit 4: Trends in medical scheme costs drivers (from 2000 to 2011)
Source: Council for Medical Schemes (2011/2012: 119)
Specialists are the second biggest category of cost drivers that medical schemes have
no control over. This largely emanates from the fact that these suppliers have the
unrestricted latitude to prescribe a number of interventions from which they benefit
enormously economically constituting a conflict of interest. Specialists also simply
charge the member where they are being short paid by the medical schemes (also
known as double billing). Hospitals and specialists have an uncomfortably close
relationship with each other; a relationship that would not be tolerated by the
competition commissions in other industries and other countries. Exhibit 5 below
depicts the proportional representation of the private hospitals and specialists in the
cost structure of medical schemes.
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Exhibit 5: Major cost drivers in the private healthcare arena (2011/2012)
Source: CMS Annual Report (2011-2012: 116)
Because of this uneven distribution of bargaining power across the industry, as well as
the close relationship between hospitals and specialists, it is not surprising that this
industry is not responding to normal market forces as other industries do.
1.6.4. Bargaining power of customers
Members are not in a position to negotiate the services they need or the tariffs they
deem fair for the services. The problem is asymmetry of information where the technical
Fanelo James Arens: Master of Commerce Dissertation, University of Cape Town
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information about the services to members / patients resides with the medical schemes
and service providers. Medical schemes generally negotiate tariffs with private
hospitals, against the odds described above. Because of the moral hazard factor
introduced by medical insurance, patients are generally apathetic to the cost of the
health care they receive. Belonging to a medical scheme “is the most important
predictor of using a private provider, particularly for inpatient care” (Alaba & McIntyre,
2012).
Switching costs, associated with moving from one scheme to the other, are so
inconsiderable, that members are continually in a state of flux into and out of schemes,
a situation that only benefit the brokers.
1.7. Solvency levels of medical schemes
The Medical Schemes Act requires that “medical schemes maintain accumulated funds
(reserves) as a percentage of gross annual contribution of not less than 25%” (CMS
Annual Report 2011: 142). The main statutory obligation of the CMS is to ensure that
schemes at all times remain financially sound at a solvency level of above 25%.
Schemes that fall below this level are intensely monitored; which includes regular
submission of management accounts, regular meeting of the Principal Officer (PO) and
the Board of Trustees (BOT) of the scheme with the CMS, as well as quarterly
submissions of business plans. Exhibit 6 below depicts the prescribed solvency levels
in red and the industry averages of all schemes in green. Of note is that the average
solvency level of all schemes has dropped and remained under the 35% level since
2008.
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Exhibit 6: Solvency levels of schemes (2000-2011)
Source: CMS Annual Report (2011-2012: 142)
1.8. Summary of introduction
The medical scheme industry has failed to thrive and to provide competitive products.
The main factors stifling schemes growth are the following; failure of the industry to
grow members; the aging membership of medical schemes; the unusually high burden
of disease in South Africa; high medical inflation; as well as the competitive industry
forces that result in lack of responsiveness of the industry to market forces. Failure to
grow sales results in the failure to grow reserves. In the current monitoring mechanism
of medical schemes, a scheme is deemed to be failing if its solvency ratio is equal to or
below the statutory level of 25%. Raath (2010; 29) argues for a risk based monitoring
tool which considers the particular risk of each scheme. It is for this reason that this
Fanelo James Arens: Master of Commerce Dissertation, University of Cape Town
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paper explores the possibility of applying the Altman failure prediction model to the
medical scheme industry.
1.9. Objective of the study
This study has a number of interrelated objectives that seek to understand and
contextualize the Altman bankruptcy prediction model in the setting of the South African
medical schemes. The objectives are as follows:
I. To do research of the literature on the subject of corporate bankruptcy
prediction models, with a view to establishing what the latest evidence is on
the validity of the Multivariate Discriminant Analysis (MDA) models in general
and the Altman model in particular.
II. To validate the Altman Z2 model amongst medical schemes in South Africa in
terms of accurately classifying Z2-scores of ≤ 1.8 and ≥ 2.9 into the a priori
groups of failed and non-failed schemes
III. Establishing new Z2-scores (and limits) through the re-estimation of new
coefficients for the original variables (T1 to T5) in the SA medical scheme
industry: this will be achieved by rerunning the MDA model for the SA medical
schemes using the original Altman variables (T1 to T5).
IV. Establishing alternative Z2-scores (and limits): Rerunning the MDA model
using new (industry specific) variables.
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2. Literature review
When a business or an industry fails there is often a lot of speculation as to the causes
of such failure. The exact reasons for the failure are often unknown and as a result the
same mistakes can be repeated. Business failure prediction models attempt to tackle
this problem to the extent that a business tool can be used to monitor and detect early
signs of failure. However choosing between these different models for empirical
application is not always an easy task (Aziz & Humayon, 2006: 18). Predicting business
failure as early as possible is always essential, particularly in periods of financial stress
and economic upheaval (Diakomihalis, 2012: 97). Bankruptcy prediction is important for
financial information users such as investors, creditors, stakeholders, credit rating
agencies, auditors, and regulators (Lifschutz & Jacobi, 2010: 133).
The main purpose of corporate failure prediction is to have a methodological approach
which identifies and discriminates companies with a high probability of future failure
from those considered to be healthy (Amendola, Bisogno, Restaino et al, 2011: 295).
The majority of these studies have been on assessing corporate health “to predict
longevity, with less emphasis on the causes of failures” (Holt, 2013: 50).This is one of
the criticisms of business prediction failure models, that they seek to predict failure with
no sufficient understanding of the underlying causes of failure. For some companies
and industries it might be too late for any rescue operations by the time the company is
found to fall in the failed category. The counter argument to this is that most of these
models predict failure two to five years in advance, providing reasonable time to
marshal rescue efforts.
2.1. Possible Causes of Business Failures
In his work on analyzing causes of business failure, Holt (2013: 62) concluded that the
generic failure agents (GFA) are shown to be: managerial, financial, company
Fanelo James Arens: Master of Commerce Dissertation, University of Cape Town
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characteristics, and macroeconomic conditions (in order of frequency). The first three
reciprocally interact within conditions defined by the latter. Each GFA has a number of
sub-causal agents (SCA) associated with it (Holt, 2013: 60). Holt suggests that
“innovation can potentially mitigate GFA and SCA negatively or positively” (Holt, 2013:
60).
Exhibit 7 below ranks the GFAs based on percentage of frequency; illustrating that
managerial causes of business failure contribute the most at 45% followed by financial
causes at 42%.
Exhibit 7: GFA ranking table
GFA All literature
% Rank
Managerial 45 1
Financial 42 2
Macroeconomics 8 3
Company characteristics 5 4
Source: Holt G.D. (2013: 62)
Exhibit 8 below illustrates “the inter-GFA reciprocal influence with the shaded central
signifying combined failure susceptibility from all GFA combined” (Holt, 2013: 63). It is
important to note that most of the SCAs constitute the five financial ratios in the Altman
model which are profitability, liquidity, low asset / high debt, capital turnover ratios, and
poor revenue vs. liabilities. In this model, innovation plays an important role in
aggravating or mitigating the impact of the GFA/CSAs.
Understanding this model can assist in conceptualizing and implementing turnaround
strategies for a company once the company has been categorized as distressed or
bankrupt by the Altman failure model. For instance, one of the indicators of financial
weaknesses is inadequate working capital amongst other things. Inadequate working
capital can be a sign of other problems in the business such poor financial management
and procurement strategies. This GFA/CSAs causal agent model also lends support to
Fanelo James Arens: Master of Commerce Dissertation, University of Cape Town
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the criticism that macroeconomic factors are not well represented in most of the earlier
bankruptcy prediction models.
Exhibit 8: Model of causal agents (GFA/CSA)
Source: Holt, G.D. (2013: 62)
Holt (2013: 65) suggests broad practical considerations to help negate the potential
negative effects of GFA (and respective SCAs). The recommendations suggest
mitigating measures according to the particular GFA implicated in the framework. The
following is a summarized version of Holt‟s framework (Holt 2013: 65).
Fanelo James Arens: Master of Commerce Dissertation, University of Cape Town
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GFA1 managerial: select work of a type and within geographic areas that offer the
organization optimum cost control, maintain up-to-date knowledge on demand,
competition, clients and suppliers and sustain positive cash flow. Embracing all of these
propositions simultaneously is a function of managerial risk minimization /mitigation.
GFA2 financial: maintain effective forecasting and accounting functions, closely monitor
liquidity, avoid high gearing; achieve appropriate returns on operating resources, control
income (which includes effective debtor management), avoid poor revenue versus
liabilities and avoid under capitalization.
GFA4 company characteristics: interact effectively with all aspects of the business
operating environment and strive for organizational learning.
GFA3 macroeconomic environment: maintain a business strategy that mitigates the
potentially negative impacts, especially from: increased competition, decreasing price
levels, high costs of borrowing, legislation, recession, and any other “shocks”.
2.2. Statistical basis of the earlier business failure prediction models
The fundamental basis of most business failure prediction models is to examine and
quantify the independent variables which are effective indicators and predictors of
business failure or distress (Altman, 2000: 1). Financial ratios are the key input
variables in most of these models. It is the link between financial ratios and statistical
techniques that are the essence of statistical bankruptcy prediction modeling.
2.3. Bridging the gap between financial ratio analysis and the more rigorous statistical techniques
Financial ratios are commonly used by accountants, managers and analysts to varying
degrees of understanding and consistency. The use of these ratios often pivots around
Fanelo James Arens: Master of Commerce Dissertation, University of Cape Town
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the comparison of companies in the same industry. The information gathered from such
analysis is barely helpful in understanding the weaknesses and strengths of a company
and is of limited use in analyzing the strategic context of a company. As Edward Altman
observed, from the 1960‟s and more so in the 1990‟s, “academics seem to be moving
towards the elimination of financial ratios as an analytical technique in assessing the
performance of the business enterprise” (Altman, 2000: 1). Altman (2000) further
observed that these academics have started to employ more statistical techniques in
explaining and predicting the performance of corporates, often in ways that financial
ratios are unable to do. The drawback of such statistical techniques has been that they
have not succeeded in finding their way into everyday business practice. The chasm
created by these divergent methods of business analysis has been of concern, as there
are merits in both approaches. Hence Altman‟s question, “Can we bridge the gap
between financial ratio analysis and the more rigorous statistical techniques which have
become popular amongst academics in more recent years?” (Altman, 2000: 2).
2.4. Univariate vs. Multivariate Analysis models
Edward Altman, who is well recognized for his work in predictive failure models since
the 1960‟s, contributed a great deal to the most used model known as the Z-score,
which primarily utilizes financial ratios in the predictive model. One of the original works
in the area of ratio analysis and bankruptcy classification was by Beaver (1967), in
which his univariate statistical analysis of bankruptcy predictors “set the stage for
Altman and other authors that followed” (Altman, 2000: 2). Beaver found that a number
of ratios could predict failure in firms for as long as five years prior to bankruptcy
(Beaver, 1968: 191). In 1972 Deakin, following up on Beaver‟s work, utilized the same
independent variables used by Beaver in 1968 within a number of multivariate
discriminant models (Deakin, 1972). The problem of using financial ratios as mentioned
above is inconsistency which may lead to instances of under estimating or over
estimating the bankruptcy risk. Altman also has concerns with univariate analysis of
Fanelo James Arens: Master of Commerce Dissertation, University of Cape Town
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financial ratios in bankruptcy prediction models for the reasons that the modeling is
prone to faulty interpretation and is potentially confusing. Altman argues that “firms with
poor profitability and/or solvency record may be regarded as potentially bankrupt,
however because of their above average liquidity, the situation may not be regarded as
that serious” (Altman, 2000: 8). Multivariate analysis on the other hand introduces the
contentious questions of “which ratios are most important in detecting bankruptcy, what
weight should be attached to these selected ratios and how should the weights be
objectively established” (Altman, 2000: 9). According to Altman, “the importance of the
multivariate discriminant analytical (MDA) remains its ability to separate companies into
failed and non-failed entities using multivariate measures” (Altman, 1968: 597).
Four out of the five variables (excluding sales / total assets) considered in the Altman
model showed significant differences between the failed and non-failed companies
(Altman, 1968: 596). Although the fifth variable (sales / total assets) did not display
significant differences between failed and non-failed firms, the significance of its
contribution to the model made Altman consider it for inclusion in the model.
2.5. Description of commonly used statistical failure prediction models
The Z-score, used by Altman (1968) in his study of manufacturing firms, uses MDA
statistical techniques. MDA in its simplest form is the comparison of two or more
independent variables between two entities in order to arrive at two estimates, which
are in turn compared for statistically significant differences. Altman describes MDA as a
“statistical technique used to classify observations into one or several a priori groupings,
dependent on the observed individual characteristics” (Altman, 2000: 9). A prior
groupings in this case meaning predetermined groupings such as male and female or
medicine „A‟ and medicine „B‟, or in the case of this study “failed and non-failed
schemes”. The shortcomings of univariate studies is that they only “consider
measurements used for group assignments; one at a time” (Altman, 2000: 9). The main
advantage of MDA in classification problems is “the potential of analyzing the entire
Fanelo James Arens: Master of Commerce Dissertation, University of Cape Town
29
variable profile of the object simultaneously rather than sequentially examining its
individual characteristics” (Altman, 2000: 9). The other advantage is that ratios are dealt
with holistically; thereby addressing the problem of inconsistency. According to Altman
(2000: 9), the discriminant function of the model transforms the individual independent
variables into a single discriminant score, or Z-value which is then used to classify the
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9. ANNEXURES
9.1. Annexure A
List of all failed schemes in order of the year they were registered.
Name of Medical Scheme Type Year Began Year Failed
Vulamed Medical Aid Society OPEN 2002/2003 2002/2003 Pretoria Municipal Medical Aid (PRETMED) OPEN 2002/2003 2003/2004 AllCare Chamber Medical Aid Scheme OPEN 2002/2003 2003/2004 Visimed Medical Scheme OPEN 2002/2003 2004/2005 Omnihealth OPEN 2002/2003 2005/2006 Medical Expenses Distribution Society (MEDS) OPEN 2002/2003 2005/2006 Free State Medical Aid Scheme OPEN 2002/2003 2005/2006 Protector Health OPEN 2002/2003 2006/2007 Meridian Health OPEN 2002/2003 2007/2008 Commercial and Industrial Medical Aid Society (CIMAS) OPEN 2002/2003 2007/2008 Global Health OPEN 2002/2003 2007/2008 Lifemed Medical Scheme OPEN 2002/2003 2007/2008 KwaZulu-Natal Medical Aid Scheme OPEN 2002/2003 2008/2009 MethealthOpenplan Medical Scheme OPEN 2002/2003 2008/2009 X-Press Care Medical Scheme OPEN 2002/2003 2008/2009 Pathfinder Medical Scheme OPEN 2002/2003 2008/2009 Telemed OPEN 2002/2003 2009/2010 NBC Medical Scheme OPEN 2002/2003 2009/2010 Medicover 2000 OPEN 2002/2003 2009/2010 Caremed Medical Scheme OPEN 2002/2003 2010/2011 Gen-Health Medical Scheme OPEN 2002/2003 2010/2011 Ingwe Health Plan OPEN 2002/2003 2010/2011 Pulz Medical Scheme OPEN 2003/2004 2004/2005 Baymed OPEN 2004/2005 2006/2007 Eclipse Medical Scheme OPEN 2004/2005 2006/2007 KPMG Medical Aid Society RESTRICTED 2002/2003 2002/2003 Ammosal Benefit Society RESTRICTED 2002/2003 2002/2003 Independent Newspapers Medical Aid Scheme RESTRICTED 2002/2003 2002/2003 NBS/BOE Group Medical Aid Fund RESTRICTED 2002/2003 2002/2003 Da Gama Medical Scheme RESTRICTED 2002/2003 2002/2003 Universal Medical Scheme RESTRICTED 2002/2003 2002/2003 Aumed Medical Aid Scheme RESTRICTED 2002/2003 2002/2003 Jomed Medical Scheme RESTRICTED 2002/2003 2003/2004 Highveld Medical Scheme RESTRICTED 2002/2003 2003/2004 Billmed Medical Scheme RESTRICTED 2002/2003 2004/2005 Anglogold Medical Scheme (Goldmed) RESTRICTED 2002/2003 2004/2005 ABI Medical Aid Scheme RESTRICTED 2002/2003 2004/2005 G5Med RESTRICTED 2002/2003 2005/2006 Venda Police and Prisons Medical Scheme (Polprismed) RESTRICTED 2002/2003 2005/2006 Klerksdorp Medical Benefit Scheme (KDM) RESTRICTED 2002/2003 2006/2007 Mutual & Federal Medical Aid Fund RESTRICTED 2002/2003 2007/2008 Ellerines Holdings Medical Aid Society RESTRICTED 2002/2003 2007/2008 CSIR Medical Scheme RESTRICTED 2002/2003 2007/2008 Chamber of Mines Medical Aid Society RESTRICTED 2002/2003 2008/2009 Johannesburg Metropolitan Chamber of Commerce and Industry Medical Aid Society
RESTRICTED 2002/2003 2008/2009
Cawmed Medical Scheme RESTRICTED 2002/2003 2008/2009 Samancor Health Plan RESTRICTED 2002/2003 2008/2009 Stocksmed RESTRICTED 2002/2003 2009/2010 Alliance Midmed Medical Scheme RESTRICTED 2002/2003 2009/2010 MEDCOR RESTRICTED 2002/2003 2009/2010 Umed RESTRICTED 2002/2003 2010/2011 Alpha Group Medical Scheme RESTRICTED 2002/2003 2010/2011 Clicks Group Medical Scheme RESTRICTED 2002/2003 2010/2011 Built Environment Professional Associations Medical Scheme (BEPS) RESTRICTED 2003/2004 2010/2011 Solvita Medical Scheme RESTRICTED 2008/2009 2009/2010
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9.2. Annexure B
The following tables are comparisons of the medians of the variables (T1 to T5) and Z-
scores of failed and non-failed schemes (open and restricted), using the Mann-Whitney
test in the period 2002/2003 to 2011/2012.
Non-Failed Schemes
Type Variable N Min Max Mean Std Dev. Median 25th
Percentile
75th
Percentile
Open
T1 26 -0.08 0.10 -0.01 0.05 -0.01 -0.04 0.02
T2 26 -0.42 0.74 0.09 0.19 0.05 0.02 0.12
T3 26 -0.51 0.36 0.00 0.14 -0.01 -0.03 0.06
T4 25 1.49 19.94 5.72 4.92 3.83 2.40 6.80
T5 26 0.05 160.13 16.53 35.91 3.85 1.25 5.56
Restricted
T1 71 -0.14 0.12 -0.01 0.05 -0.01 -0.04 0.01
T2 71 -0.12 0.48 0.07 0.10 0.06 0.01 0.12
T3 71 -0.59 0.45 0.00 0.13 0.01 -0.06 0.08
T4 70 0.27 69.60 11.57 11.53 7.62 3.76 15.87
T5 71 0.01 893.01 18.94 105.82 1.97 0.66 7.04
Total
T1 97 -0.14 0.12 -0.01 0.05 -0.01 -0.04 0.01
T2 97 -0.42 0.74 0.08 0.13 0.06 0.02 0.12
T3 97 -0.59 0.45 0.00 0.13 0.00 -0.05 0.07
T4 95 0.27 69.60 10.03 10.51 5.78 3.21 14.04
T5 97 0.01 893.01 18.29 92.21 2.30 0.87 6.17
Failed Schemes
Type Variable N Min Max Mean Std Dev. Median 25th
Percentile
75th
Percentile
Open
T1 15 -4.24 0.49 -0.29 1.11 0.00 -0.11 0.02
T2 15 -4.06 0.23 -0.33 1.08 -0.01 -0.11 0.12
T3 15 -4.07 0.21 -0.40 1.08 -0.09 -0.18 0.07
T4 15 -5.87 27.67 3.28 7.38 1.50 0.35 4.05
T5 15 0.31 13.91 3.62 3.93 2.22 1.31 4.15
Restricted
T1 15 -0.06 0.21 0.03 0.06 0.02 0.00 0.05
T2 16 -0.63 0.25 0.01 0.20 0.02 -0.04 0.15
T3 16 -0.75 0.21 -0.09 0.24 -0.03 -0.12 0.01
T4 14 0.16 26.17 5.94 7.45 2.37 1.77 6.75
T5 15 0.00 4.80 1.20 1.19 0.80 0.73 1.09
Total
T1 30 -4.24 0.49 -0.13 0.79 0.00 -0.03 0.04
T2 31 -4.06 0.25 -0.15 0.77 0.00 -0.09 0.12
T3 31 -4.07 0.21 -0.24 0.77 -0.05 -0.15 0.03
T4 29 -5.87 27.67 4.56 7.40 2.09 0.82 4.58
T5 30 0.00 13.91 2.41 3.11 1.20 0.75 3.03
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9.3. Annexure C
The table below illustrates classification and error rates as well as percentage of
unclassifiable schemes
Actual Year Prediction(years prior to failure)
Type of scheme Classified Companies Unable to classify
Classification Rate Error rate
2003/2004 2 All Schemes NA NA NA
Open NA NA NA
Restricted NA NA NA
1 All Schemes 84% 16% 43%
Open 81% 19% 66%
Restricted 85% 15% 30%
2004/2005 2 All Schemes 84% 16% 43%
Open 80% 20% 67%
Restricted 84% 16% 29%
1 All Schemes 92% 8% 4%
Open 87% 13% 0%
Restricted 95% 5% 6%
2005/2006 2 All Schemes 45% 55% 4%
Open 81% 19% 0%
Restricted 95% 5% 6%
1 All Schemes 46% 54% 10%
Open 82% 18% 6%
Restricted 93% 7% 12%
2006/2007 2 All Schemes 86% 14% 11%
Open 80% 20% 7%
Restricted 90% 10% 13%
1 All Schemes 83% 17% 28%
Open 78% 22% 26%
Restricted 86% 14% 29%
2007/2008 2 All Schemes 83% 17% 28%
Open 80% 20% 27%
Restricted 84% 16% 28%
1 All Schemes 88% 12% 31%
Open 85% 15% 10%
Restricted 90% 10% 29%
2008/2009 2 All Schemes 88% 12% 30%
Open 88% 13% 33%
Restricted 88% 12% 28%
1 All Schemes 84% 16% 26%
Open 79% 21% 22%
Restricted 86% 14% 28%
2009/2010 2 All Schemes 86% 14% 27%
Open 80% 20% 24%
Restricted 89% 11% 28%
1 All Schemes 85% 15% 30%
Open 80% 20% 35%
Restricted 87% 13% 27%
2010/2011 2 All Schemes 89% 11% 28%
Open 89% 11% 36%
Restricted 89% 11% 25%
1 All Schemes 87% 13% 27%
Open 88% 13% 20%
Restricted 86% 14% 30%
2011/2012 2 All Schemes 93% 7% 28%
Open 96% 5% 22%
Restricted 92% 8% 30%
1 All Schemes 93% 7% 21%
Open 95% 5% 15%
Restricted 93% 7% 23%
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9.4. Annexure D
This annexure shows the re-substitution and leave-one-out classifications and posterior
probabilities for those observations that were misclassified by the LDA model.
Obs Classification Probabilities LOO Probabilities
TRUE Class LOO Cl. 0 1 0 1
1 1 0 * 0 * 0.5571 0.4429 0.5881 0.4119
3 1 0 * 0 * 0.7244 0.2756 0.7698 0.2302
4 1 0 * 0 * 0.6974 0.3026 0.7177 0.2823
5 1 0 * 0 * 0.7948 0.2052 0.8479 0.1521
7 1 0 * 0 * 0.6258 0.3742 0.6526 0.3474
10 1 0 * 0 * 0.6273 0.3727 0.6484 0.3516
13 1 0 * 0 * 0.5443 0.4557 0.5764 0.4236
15 1 1 0 * 0.4513 0.5487 0.53 0.47
16 1 0 * 0 * 0.5802 0.4198 0.5924 0.4076
17 1 0 * 0 * 0.6294 0.3706 0.6413 0.3587
19 1 0 * 0 * 0.561 0.439 0.5815 0.4185
20 1 0 * 0 * 0.5798 0.4202 0.5998 0.4002
22 1 0 * 0 * 0.6055 0.3945 0.6269 0.3731
23 1 0 * 0 * 0.5993 0.4007 0.6156 0.3844
25 1 0 * 0 * 0.5891 0.4109 0.6311 0.3689
26 1 0 * 0 * 0.5584 0.4416 0.5627 0.4373
28 1 0 * 0 * 0.5308 0.4692 0.5427 0.4573
29 1 0 * 0 * 0.6287 0.3713 0.6478 0.3522
31 1 0 * 0 * 0.5092 0.4908 0.52 0.48
32 1 0 * 0 * 0.6948 0.3052 0.7152 0.2848
34 1 0 * 0 * 0.5512 0.4488 0.6029 0.3971
51 0 1 * 1 * 0.391 0.609 0.3801 0.6199
54 0 1 * 1 * 0.4514 0.5486 0.4293 0.5707
57 0 1 * 1 * 0.4529 0.5471 0.4435 0.5565
58 0 1 * 1 * 0.4908 0.5092 0.4837 0.5163
62 0 1 * 1 * 0.0801 0.9199 0.0256 0.9744
72 0 1 * 1 * 0.4082 0.5918 0.0802 0.9198
77 0 1 * 1 * 0.4702 0.5298 0.4684 0.5316
82 0 1 * 1 * 0.4844 0.5156 0.4811 0.5189
98 0 1 * 1 * 0.4601 0.5399 0.4529 0.5471
100 0 1 * 1 * 0.4648 0.5352 0.4302 0.5698
102 0 1 * 1 * 0.3553 0.6447 0.3446 0.6554
103 0 1 * 1 * 0.374 0.626 0.3285 0.6715
105 0 1 * 1 * 0.4338 0.5662 0.4254 0.5746
109 0 1 * 1 * 0.466 0.534 0.4606 0.5394
112 0 1 * 1 * 0.485 0.515 0.4455 0.5545
115 0 1 * 1 * 0.4275 0.5725 0.418 0.582
118 0 1 * 1 * 0.199 0.801 0.178 0.822
119 0 1 * 1 * 0.4566 0.5434 0.4337 0.5663
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9.5. Annexure E
This annexure shows the re-substitution and leave-one-out classifications and posterior
probabilities for those observations that were misclassified by the LDA model whilst re-
establishing the Alt_MS_Z-score.
Obs Classification Probabilities LOO Probabilities
TRUE Class LOO Cl. 0 1 0 1
1 1 1 0 * 0.4996 0.5004 0.5266 0.4734
3 1 0 * 0 * 0.8104 0.1896 0.9534 0.0466
4 1 0 * 0 * 0.549 0.451 0.5834 0.4166
5 1 0 * 0 * 0.9548 0.0452 0.9798 0.0202
10 1 0 * 0 * 0.6844 0.3156 0.7089 0.2911
17 1 0 * 0 * 0.8427 0.1573 0.865 0.135
20 1 0 * 0 * 0.5772 0.4228 0.6019 0.3981
22 1 0 * 0 * 0.6086 0.3914 0.6411 0.3589
23 1 0 * 0 * 0.6965 0.3035 0.7226 0.2774
24 1 0 * 0 * 0.5547 0.4453 0.5721 0.4279
26 1 0 * 0 * 0.5631 0.4369 0.5733 0.4267
28 1 0 * 0 * 0.65 0.35 0.6712 0.3288
29 1 0 * 0 * 0.6921 0.3079 0.7202 0.2798
30 1 0 * 0 * 0.5774 0.4226 0.5979 0.4021
32 1 0 * 0 * 0.7078 0.2922 0.7346 0.2654
34 1 0 * 0 * 0.6124 0.3876 0.7133 0.2867
35 1 0 * 0 * 0.5245 0.4755 0.5404 0.4596
38 1 0 * 0 * 0.5614 0.4386 0.5757 0.4243
51 0 1 * 1 * 0.4239 0.5761 0.4112 0.5888
54 0 0 1 * 0.508 0.492 0.4887 0.5113
60 0 1 * 1 * 0.4966 0.5034 0.4431 0.5569
62 0 1 * 1 * 0.1036 0.8964 0.0502 0.9498
70 0 1 * 1 * 0.142 0.858 0.1057 0.8943
72 0 1 * 1 * 0.1855 0.8145 0.0554 0.9446
78 0 1 * 1 * 0.3352 0.6648 0.3036 0.6964
98 0 1 * 1 * 0.3867 0.6133 0.3717 0.6283
100 0 1 * 1 * 0.4105 0.5895 0.3927 0.6073
102 0 1 * 1 * 0.4316 0.5684 0.4208 0.5792
103 0 0 1 * 0.5016 0.4984 0.4906 0.5094
112 0 1 * 1 * 0.4415 0.5585 0.424 0.576
115 0 1 * 1 * 0.4894 0.5106 0.4822 0.5178
118 0 1 * 1 * 0.2938 0.7062 0.2774 0.7226
119 0 0 1 * 0.5069 0.4931 0.4793 0.5207
Fanelo James Arens: Master of Commerce Dissertation, University of Cape Town